A recursive local search method of separators for Bayesian network decomposition structure learning algorithm

The decomposition structure learning algorithm is the most effective for the structure learning of large Bayesian networks. Maximal prime subgraph decomposition is one of the main methods of Bayesian network structure decomposition learning. The key to maximal prime subgraph decomposition is the search for separators. However, existing methods of searching separators are inefficient, because they all search for separators globally. To improve the accuracy and speed of Bayesian network structure decomposition learning algorithm, we design an efficient recursive Bayesian network structure decomposition learning algorithm (ERDA) and propose a method to locally search for separators recursively for ERDA in this paper. Each iteration includes two steps. The first stage is to determine a target node according to the minimum node degree. The second stage is to perform a local search for the separator in the adjacent node set of the target node. The separator splits the network into two subgraphs, where the small subgraph contains the target node and the larger one does not. Local search is only performed iteratively in the large subgraph. Finally, we conduct experiments on various samples to compare the Hamming distance and running time of ERDA method with four existing methods and ERDA method based on recursive local search for separators with ERDA based on global search for separators. Then, we apply our method to the German credit dataset, which is a real data from UCI, to obtain its credit causality model. All the algorithms are compiled and implemented in MATLAB. Experiments show that our method has better performance than state-of-the-art methods and has applicability to real problems.